How do I reset a specific bone's "Stretch To" Rest Length, via code?
When running from the properties constraints panel context.constraint is defined.  To run in script elsewhere we need to override context ie add constraint to the context dictionary and pass it to the operator. 

c = context.copy()  # copy the context returns dic.
# add constraint to the context dictionary
c["constraint"] = context.active_pose_bone.constraints['Stretch To']
# override context by passing dic as first argument
bpy.ops.constraint.stretchto_reset(c, constraint="Stretch To", owner='BONE')


Note: the code above is using the selected and active pose bone. There are numerous otherways to select and send a particular pose bone to the operator.